Q.1 (iv) The perpendicular distance of the plane bar r·(2hat i+3hat j-hat k)=5 from the origin is ____. A. 5/√(14) units B. 5/14 units C. 5 units D. √(14)/5 units

Chapter: Line and Plane· Mathematics & Statistics Part 1

The perpendicular distance of the plane \(\bar r\cdot(2\hat i+3\hat j-\hat k)=5\) from the origin is ____.

Q.1 (iv) The perpendicular distance of the plane \(\bar r\cdot(2\hat i+3\hat j-\hat k)=5\) from the origin is ____.

A. \(\dfrac{5}{\sqrt{14}}\) units

B. \(\dfrac{5}{14}\) units

C. 5 units

D. \(\dfrac{\sqrt{14}}{5}\) units

Doubtly Asked 29 Oct 2026 Board exam · July 2024 hsc 12th Save WhatsApp Report

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Answer: A. \(\dfrac{5}{\sqrt{14}}\) units

Answer: (a) \(\dfrac{5}{\sqrt{14}}\) units

For the plane \(\bar r\cdot\bar n=d\), the distance from the origin is \(\dfrac{|d|}{|\bar n|}\). Here \(|\bar n|=\sqrt{4+9+1}=\sqrt{14}\) and \(d=5\), so the distance is \(\dfrac{5}{\sqrt{14}}\) units.

Doubtly AI · 29 Oct 2026 AI-generated · not yet verified Report

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The perpendicular distance of the plane \(\bar r\cdot(2\hat i+3\hat j-\hat k)=5\) from the origin is ____.

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